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{composition-setup}{composition-setup}
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h1. Momentum and External Force


h4. Description and Assumptions
{excerpt:hidden=true}*[*System*|system]**:* Any. --- *[*Interactions*|interaction]**:* Any. --- *Note:* Linear [momentum|momentum] evolves separately from [angular momentum|angular momentum about a single axis], so all system constituents are treated as [point particles|point particle] in this [model|model].{excerpt}
This [model|model] is generally applicable (assuming knowledge of the external [forces|force] and [system|system] [constituents|system constituent]).

h4. Problem Cues

This [model|model] is especially useful when describing the [momentum|momentum] of [systems|system] where [external forces|external force] are absent ([system|system] [momentum|momentum] will be constant) or estimating the [force|force] in a process that occurs in a very short time interval such as collisions ([impulse|impulse] will be easier to determine than [force|force]).

h4. Learning Objectives

Students will be assumed to understand this model who can:
* Define the momentum of a [point particle].
* Define [impulse] in terms of [momentum] or in terms of [force].
* Give an expression for the time-average [force] on a [system] in terms of its [momentum].
* Calculate the net [external force] on a [system] containing several objects.
* Describe the conditions required for the [momentum] of a [system] to be [conserved].
* Describe the [system] that must be considered and the assumptions that lead to approximate conservation of momentum in a collision.

h2. Model


h4. Compatible Systems

The system must be effectively composed of [point particles|point particle], though rigid bodies may be treated as point particles with positions specified by the center of mass positions of the rigid body when this model is used.

h4. Relevant Interactions

Only [external forces|external force] need be considered, since [internal forces|internal force] do not change the system's momentum.

h4. Relevant Definitions
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{latex}\begin{large}\[ \vec{p} = m\vec{v}\]\end{large}{latex}

h4. Laws of Change

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h6. Differential Form

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{latex}\begin{large}\[ \sum_{\rm system}\frac{d\vec{p}}{dt} = \sum_{\rm external} \vec{F}\]\end{large}{latex}
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h6. Integral Form

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{latex}\begin{large}\[ \sum_{\rm system}\vec{p}_{f} = \sum_{\rm system}\vec{p}_{i} + \sum_{\rm external} \vec{J} = \sum_{\rm system}\vec{p}_{i} + \int \sum_{\rm external} \vec{F}\:dt  \]
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h4. Diagrammatic Representations

* [initial-state final-state diagram]
* [free body diagram]

h1. Relevant Examples


h4. {toggle-cloak:id=const} Examples Involving Constant Momentum

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{contentbylabel:constant_momentum|showSpace=false|showLabels=true|excerpt=true|maxResults=50}
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h4. {toggle-cloak:id=imp} Examples Involving Impulse

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{contentbylabel:impulse|showSpace=false|showLabels=true|excerpt=true|maxResults=50}
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h4. {toggle-cloak:id=oned} Examples Involving 1-D Collisions

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{contentbylabel:1d_collision|showSpace=false|showLabels=true|excerpt=true|maxResults=50}
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h4. {toggle-cloak:id=twod} Examples Involving 2-D Collisions

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{contentbylabel:2d_collision|showSpace=false|showLabels=true|excerpt=true|maxResults=50}
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h4. {toggle-cloak:id=elas} Examples Involving Elastic Collisions

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{contentbylabel:elastic_collision|showSpace=false|showLabels=true|excerpt=true|maxResults=50}
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h4. {toggle-cloak:id=inel} Examples Involving Totally Inelastic Collisions

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{contentbylabel:totally_inelastic|showSpace=false|showLabels=true|excerpt=true|maxResults=50}
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h4. {toggle-cloak:id=flux} Examples Involving Continuous Momentum Flux

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{contentbylabel:momentum_force|showSpace=false|showLabels=true|excerpt=true|maxResults=50}
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h4. {toggle-cloak:id=all} All Examples Using this Model

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{contentbylabel:constant_momentum,momentum_force,impulse|showSpace=false|showLabels=true|excerpt=true|operator=OR|maxResults=50}
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!billiards.jpg|width=235px!\\ !skaters.jpg|width=235px!\\ !shuttle.jpg!
Photos courtesy:
* [Wikimedia Commons|http://commons.wikimedia.org] by user [No-w-ay|http://commons.wikimedia.org/wiki/User:No-w-ay] in collaboration with H. Caps
* [Wikimedia Commons|http://commons.wikimedia.org] by user [Uwe Langer|http://commons.wikimedia.org/wiki/User:Uwe_Langer]
* [NASA Johnson Space Center (NASA-JSC)|http://images.jsc.nasa.gov]
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